基于二维B-splines方法研究强磁场中类氢离子He+的低能能级

采用改进的二维B-spline方法在柱坐标系下研究了强磁场下类氢离子He^(+)的结构和电子空间几率密度,计算包含三种对称性0^(+)、0^(-)和(^(-)1)^(+)共10个本征态1 0^(+)、2 0^(+)、ν 0^(-)(ν=1~4)和ν(-1)^(+)(ν=1~4)的能级,选定磁感应强度分别为0、0.001、0.003、0.005、0.007、0.010、0.030、0.050、0.070、0.100、0.200、0.300、0.500、0.700和1.000 a.u.。计算结果表明,类氢离子He^(+)的能级在强磁场中发生劈裂,简并度消除,得到了各个能级随磁感应强度变化规律,并且发现随着磁感应强度的增加能级高低会改变,甚至会发生能级翻转现象;定量地研究了类氢离子He^(+)的基态1 0^(+)和激发态3 0^(-)几率密度分布随磁感应强度的变化规律,并与氢原子进行比较。本研究部分计算结果与他人研究结果十分吻合,有助于进一步理解其他复杂原子的电子运动行为。

B-Spline曲线聚风装置直线翼垂直轴风力机启动性能数值模拟

为了提升直线翼垂直轴风力机的启动性能,基于B-Spline曲线生成方法,提出一种具有流线型轮廓的聚风装置,将其分别安装在风轮顶端和底端,用以提升风轮附近的来流风速,使风轮汲取更多风能,达到更易启动的特点.选取聚风装置的5个结构参数进行设计:聚风装置与风轮间隙距离ΔL、底圆半径R_(1)、顶圆半径R_(2)、入口角度α_(1)和出口角度α_(2).设计方法采用二次旋转正交组合筛选最优模型,通过三维数值模拟研究聚风装置参数对直线翼垂直轴风力机启动性能的影响,获得了最佳外形参数组合.此外,对有无加装聚风装置的直线翼垂直轴风力机进行了静态三维数值模拟.结果表明,通过添加具有外凸流线型轮廓的聚风装置,直线翼垂直轴风力机的启动性能有显著提升.在风速较低的情况下,性能改善更加明显.聚风装置可使直线翼垂直轴风力机的平均启动力矩系数最大增加38.8%,峰值平均启动力矩系数最大可增加31.2%.

An Efficient Numerical Scheme for Biological Models in the Frame of Bernoulli Wavelets

This article considers three types of biological systems:the dengue fever disease model,the COVID-19 virus model,and the transmission of Tuberculosis model.The new technique of creating the integration matrix for the Bernoulli wavelets is applied.Also,the novel method proposed in this paper is called the Bernoulli wavelet collocation scheme(BWCM).All three models are in the form system of coupled ordinary differential equations without an exact solution.These systems are converted into a system of algebraic equations using the Bernoulli wavelet collocation scheme.The numerical wave distributions of these governing models are obtained by solving the algebraic equations via the Newton-Raphson method.The results obtained from the developed strategy are compared to several schemes such as the Runge Kutta method,and ND solver in mathematical software.The convergence analyses are discussed through theorems.The newly implemented Bernoulli wavelet method improves the accuracy and converges when it is compared with the existing methods in the literature.

ASTER Data Processing by Discrete Wavelets Transform and Band Ratio Techniques for the Identification of Lineaments and Hydrothermal Alteration Zones in Poli, North Cameroon

The aim of this study is to carry out hydrothermal alteration mapping and structural mapping using ASTER images in order to identify indices that could guide mining exploration work in the Poli area and its surroundings. To achieve this, the ASTER images were first preprocessed to correct atmospheric effects and remove vegetation influence. Secondly, a lineament mapping was conducted by applying Discrete Wavelet Transform (DWT) algorithms to the First Principal Component Analysis (PCA1) of Visible Near-Infrared (VNIR) and Shortwave Infrared (SWIR) bands. Lastly, band ratio methods were applied to the VNIR, SWIR, and Thermal Infrared (TIR) bands to determine indices of iron oxides/hydroxides (hematite and limonite), hydroxyl-bearing minerals (chlorite, epidote, and muscovite), and the quartz index. The results obtained showed that the lineaments were mainly oriented NE-SW, ENE-WSW, and E-W, with NE-SW being the most predominant direction. Concerning hydrothermal alteration, the identified indices covered almost the entire study area and showed a strong correlation with lithological data. Overlaying the obtained lineaments with the hydrothermal alteration indices revealed a significant correlation between existing mining indices and those observed in the field. Mineralized zones generally coincided with areas of high lineament density exhibiting significant hydrothermal alteration. Based on the correlation between existing mining indices and the results of hydrothermal and structural mapping, the results obtained can then be used as a reference document for any mining exploration in the study area.

A Study on B-Spline Wavelets and Wavelet Packets

In this paper, we discuss the B-spline wavelets introduced by Chui and Wang in [1]. The definition for B-spline wavelet packets is proposed along with the corresponding dual wavelet packets. The properties of B-spline wavelet packets are also investigated.

WT-FCTGN:A wavelet-enhanced fully connected time-gated neural network for complex noisy traffic flow modeling

Accurate forecasting of traffic flow provides a powerful traffic decision-making basis for an intelligent transportation system. However, the traffic data's complexity and fluctuation, as well as the noise produced during collecting information and summarizing original data of traffic flow, cause large errors in the traffic flow forecasting results. This article suggests a solution to the above mentioned issues and proposes a fully connected time-gated neural network based on wavelet reconstruction(WT-FCTGN). To eliminate the potential noise and strengthen the potential traffic trend in the data, we adopt the methods of wavelet reconstruction and periodic data introduction to preprocess the data. The model introduces fully connected time-series blocks to model all the information including time sequence information and fluctuation information in the flow of traffic, and establishes the time gate block to comprehend the periodic characteristics of the flow of traffic and predict its flow. The performance of the WT-FCTGN model is validated on the public Pe MS data set. The experimental results show that the WT-FCTGN model has higher accuracy, and its mean absolute error(MAE), mean absolute percentage error(MAPE) and root mean square error(RMSE) are obviously lower than those of the other algorithms. The robust experimental results prove that the WT-FCTGN model has good anti-noise ability.

Image Hiding with High Robustness Based on Dynamic Region Attention in the Wavelet Domain

Hidden capacity,concealment,security,and robustness are essential indicators of hiding algorithms.Currently,hiding algorithms tend to focus on algorithmic capacity,concealment,and security but often overlook the robustness of the algorithms.In practical applications,the container can suffer from damage caused by noise,cropping,and other attacks during transmission,resulting in challenging or even impossible complete recovery of the secret image.An image hiding algorithm based on dynamic region attention in the multi-scale wavelet domain is proposed to address this issue and enhance the robustness of hiding algorithms.In this proposed algorithm,a secret image of size 256×256 is first decomposed using an eight-level Haar wavelet transform.The wavelet transform generates one coefficient in the approximation component and twenty-four detail bands,which are then embedded into the carrier image via a hiding network.During the recovery process,the container image is divided into four non-overlapping parts,each employed to reconstruct a low-resolution secret image.These lowresolution secret images are combined using densemodules to obtain a high-quality secret image.The experimental results showed that even under destructive attacks on the container image,the proposed algorithm is successful in recovering a high-quality secret image,indicating that the algorithm exhibits a high degree of robustness against various attacks.The proposed algorithm effectively addresses the robustness issue by incorporating both spatial and channel attention mechanisms in the multi-scale wavelet domain,making it suitable for practical applications.In conclusion,the image hiding algorithm introduced in this study offers significant improvements in robustness compared to existing algorithms.Its ability to recover high-quality secret images even in the presence of destructive attacksmakes it an attractive option for various applications.Further research and experimentation can explore the algorithm’s performance under different scenarios and expand its potential applications.

A lightweight symmetric image encryption cryptosystem in wavelet domain based on an improved sine map

In the era of big data,the number of images transmitted over the public channel increases exponentially.As a result,it is crucial to devise the efficient and highly secure encryption method to safeguard the sensitive image.In this paper,an improved sine map(ISM)possessing a larger chaotic region,more complex chaotic behavior and greater unpredictability is proposed and extensively tested.Drawing upon the strengths of ISM,we introduce a lightweight symmetric image encryption cryptosystem in wavelet domain(WDLIC).The WDLIC employs selective encryption to strike a satisfactory balance between security and speed.Initially,only the low-frequency-low-frequency component is chosen to encrypt utilizing classic permutation and diffusion.Then leveraging the statistical properties in wavelet domain,Gaussianization operation which opens the minds of encrypting image information in wavelet domain is first proposed and employed to all sub-bands.Simulations and theoretical analysis demonstrate the high speed and the remarkable effectiveness of WDLIC.

Olive Leaf Disease Detection via Wavelet Transform and Feature Fusion of Pre-Trained Deep Learning Models

Olive trees are susceptible to a variety of diseases that can cause significant crop damage and economic losses.Early detection of these diseases is essential for effective management.We propose a novel transformed wavelet,feature-fused,pre-trained deep learning model for detecting olive leaf diseases.The proposed model combines wavelet transforms with pre-trained deep-learning models to extract discriminative features from olive leaf images.The model has four main phases:preprocessing using data augmentation,three-level wavelet transformation,learning using pre-trained deep learning models,and a fused deep learning model.In the preprocessing phase,the image dataset is augmented using techniques such as resizing,rescaling,flipping,rotation,zooming,and contrasting.In wavelet transformation,the augmented images are decomposed into three frequency levels.Three pre-trained deep learning models,EfficientNet-B7,DenseNet-201,and ResNet-152-V2,are used in the learning phase.The models were trained using the approximate images of the third-level sub-band of the wavelet transform.In the fused phase,the fused model consists of a merge layer,three dense layers,and two dropout layers.The proposed model was evaluated using a dataset of images of healthy and infected olive leaves.It achieved an accuracy of 99.72%in the diagnosis of olive leaf diseases,which exceeds the accuracy of other methods reported in the literature.This finding suggests that our proposed method is a promising tool for the early detection of olive leaf diseases.

Deep neural network based on multi-level wavelet and attention for structured illumination microscopy

Structured illumination microscopy(SIM)is a popular and powerful super-resolution(SR)technique in biomedical research.However,the conventional reconstruction algorithm for SIM heavily relies on the accurate prior knowledge of illumination patterns and signal-to-noise ratio(SNR)of raw images.To obtain high-quality SR images,several raw images need to be captured under high fluorescence level,which further restricts SIM’s temporal resolution and its applications.Deep learning(DL)is a data-driven technology that has been used to expand the limits of optical microscopy.In this study,we propose a deep neural network based on multi-level wavelet and attention mechanism(MWAM)for SIM.Our results show that the MWAM network can extract high-frequency information contained in SIM raw images and accurately integrate it into the output image,resulting in superior SR images compared to those generated using wide-field images as input data.We also demonstrate that the number of SIM raw images can be reduced to three,with one image in each illumination orientation,to achieve the optimal tradeoff between temporal and spatial resolution.Furthermore,our MWAM network exhibits superior reconstruction ability on low-SNR images compared to conventional SIM algorithms.We have also analyzed the adaptability of this network on other biological samples and successfully applied the pretrained model to other SIM systems.

Enhanced Fourier Transform Using Wavelet Packet Decomposition

Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

AMicroseismic Signal Denoising Algorithm Combining VMD and Wavelet Threshold Denoising Optimized by BWOA

The denoising of microseismic signals is a prerequisite for subsequent analysis and research.In this research,a new microseismic signal denoising algorithm called the Black Widow Optimization Algorithm(BWOA)optimized VariationalMode Decomposition(VMD)jointWavelet Threshold Denoising(WTD)algorithm(BVW)is proposed.The BVW algorithm integrates VMD and WTD,both of which are optimized by BWOA.Specifically,this algorithm utilizes VMD to decompose the microseismic signal to be denoised into several Band-Limited IntrinsicMode Functions(BLIMFs).Subsequently,these BLIMFs whose correlation coefficients with the microseismic signal to be denoised are higher than a threshold are selected as the effective mode functions,and the effective mode functions are denoised using WTD to filter out the residual low-and intermediate-frequency noise.Finally,the denoised microseismic signal is obtained through reconstruction.The ideal values of VMD parameters and WTD parameters are acquired by searching with BWOA to achieve the best VMD decomposition performance and solve the problem of relying on experience and requiring a large workload in the application of the WTD algorithm.The outcomes of simulated experiments indicate that this algorithm is capable of achieving good denoising performance under noise of different intensities,and the denoising performance is significantly better than the commonly used VMD and Empirical Mode Decomposition(EMD)algorithms.The BVW algorithm is more efficient in filtering noise,the waveform after denoising is smoother,the amplitude of the waveform is the closest to the original signal,and the signal-to-noise ratio(SNR)and the root mean square error after denoising are more satisfying.The case based on Fankou Lead-Zinc Mine shows that for microseismic signals with different intensities of noise monitored on-site,compared with VMD and EMD,the BVW algorithm ismore efficient in filtering noise,and the SNR after denoising is higher.

Research on the longitudinal protection of a through-type cophase traction direct power supply system based on the empirical wavelet transform

This paper proposes a longitudinal protection scheme utilizing empirical wavelet transform(EWT)for a through-type cophase traction direct power supply system,where both sides of a traction network line exhibit a distinctive boundary structure.This approach capitalizes on the boundary’s capacity to attenuate the high-frequency component of fault signals,resulting in a variation in the high-frequency transient energy ratio when faults occur inside or outside the line.During internal line faults,the high-frequency transient energy at the checkpoints located at both ends surpasses that of its neighboring lines.Conversely,for faults external to the line,the energy is lower compared to adjacent lines.EWT is employed to decompose the collected fault current signals,allowing access to the high-frequency transient energy.The longitudinal protection for the traction network line is established based on disparities between both ends of the traction network line and the high-frequency transient energy on either side of the boundary.Moreover,simulation verification through experimental results demonstrates the effectiveness of the proposed protection scheme across various initial fault angles,distances to faults,and fault transition resistances.

Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems

In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.

Weak Fault Feature Extraction of the Rotating Machinery Using Flexible Analytic Wavelet Transform and Nonlinear Quantum Permutation Entropy

Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform(FAWT)with Nonlinear Quantum Permutation Entropy.FAWT,leveraging fractional orders and arbitrary scaling and translation factors,exhibits superior translational invariance and adjustable fundamental oscillatory characteristics.This flexibility enables FAWT to provide well-suited wavelet shapes,effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults.In our approach,gearbox vibration signals undergo FAWT to obtain sub-bands.Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy,a feature that more accurately characterizes the operational state of vibration simulation signals.The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery.A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method.Comparative assessments with parameters derived from traditional permutation entropy,sample entropy,wavelet transform(WT),and empirical mode decomposition(EMD)underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.

Performance of Continuous Wavelet Transform over Fourier Transform in Features Resolutions

This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic data obtained from the Tano Basin in West Africa, Ghana. The research focuses on a comparative analysis of image clarity in seismic attribute analysis to facilitate the identification of reservoir features within the subsurface structures. The findings of the study indicate that CWT has a significant advantage over FFT in terms of image quality and identifying subsurface structures. The results demonstrate the superior performance of CWT in providing a better representation, making it more effective for seismic attribute analysis. The study highlights the importance of choosing the appropriate image enhancement technique based on the specific application needs and the broader context of the study. While CWT provides high-quality images and superior performance in identifying subsurface structures, the selection between these methods should be made judiciously, taking into account the objectives of the study and the characteristics of the signals being analyzed. The research provides valuable insights into the decision-making process for selecting image enhancement techniques in seismic data analysis, helping researchers and practitioners make informed choices that cater to the unique requirements of their studies. Ultimately, this study contributes to the advancement of the field of subsurface imaging and geological feature identification.

Variational Mode Decomposition-Informed Empirical Wavelet Transform for Electric Vibrator Noise Analysis

Electric vibrators find wide applications in reliability testing, waveform generation, and vibration simulation, making their noise characteristics a topic of significant interest. While Variational Mode Decomposition (VMD) and Empirical Wavelet Transform (EWT) offer valuable support for studying signal components, they also present certain limitations. This article integrates the strengths of both methods and proposes an enhanced approach that integrates VMD into the frequency band division principle of EWT. Initially, the method decomposes the signal using VMD, determining the mode count based on residuals, and subsequently employs EWT decomposition based on this information. This addresses mode aliasing issues in the original method while capitalizing on VMD’s adaptability. Feasibility was confirmed through simulation signals and ultimately applied to noise signals from vibrators. Experimental results demonstrate that the improved method not only resolves EWT frequency band division challenges but also effectively decomposes signal components compared to the VMD method.

基于B-spline的路径规划与轨迹跟踪研究

为满足局部路径规划换道路径下的特性和提高智能驾驶车辆在多种变曲率条件下的路径跟踪精度和稳定性,采用贝塞尔曲线、B-spline等路径规划换道条件下的方法,分别在圆形轨迹、8字形轨迹、S形轨迹、正弦曲线形轨迹路径下,基于MATLAB对4类路径跟踪算法进行分析,得出最合理的B-spline路径规划和跟踪算法。结果表明,B-spline算法在换道点和并道点曲率为0,满足换道条件的要求;MPC算法在正弦轨迹下比其他算法平均误差小约48.6%,在圆形轨迹下比其他算法平均误差小约84%,说明该算法在多种轨迹下都具有很好的跟踪性,能在一定程度上保证智能驾驶汽车的安全性和稳定性,为今后智能车辆路径规划和轨迹跟踪控制研究提供参考。

基于ICEEMDAN-SSA-Wavelet的声发射信号降噪研究

针对粘接件声发射(AE)信号含有噪声分量难以滤除的问题,提出一种改进ICEEMDAN的方法。该方法首先使用ICEEMDAN分解原始AE信号,并通过相关系数和能量差值的方法筛选出低频分量和高频分量;运用麻雀优化算法(SSA)优化后的改进小波阈值去噪算法对其进行去噪;最后将保留的低频分量和去噪后的高频分量重构成一个新的信号,通过实验数据对比和分析评估降噪效果。实验结果表明,相较于改进小波阈值去噪和ICEEMDAN去噪,文中提出的方法对金属与非金属粘接件AE信号的降噪效果更好,能够保护原始信号的频域信息,进而提高脱粘检测精度。

基于Mann-Kendall和Wavelet分析的唐山市近60年来降水量时空变化研究

降水量时空变化研究,对了解和预测气候变化趋势、合理规划水资源,以及应对极端天气事件具有重要意义。基于唐山市12个标准气象站点的1961-2020年观测资料,采用Mann-Kendall和Wavelet方法相结合的方式,对唐山市降水量时变性进行分析。结果表明,近60年来研究区降水量变化斜率为-1.59mm/a,经Mann-Kendall检测的趋势值Sen’slo值为-1.23mm/a;年际降水量于2014年发生突变,但并不显著;利用Wavelet分析发现,区域降水量存在1~8、7~10、14~16年的变化周期。